{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "61e8726d",
   "metadata": {},
   "source": [
    "# 上采样"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e327a1ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x800 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 定义上采样函数（零阶保持法）\n",
    "def upsampling_zero_order_hold(x, factor):\n",
    "    N = len(x)\n",
    "    y = np.zeros(N * factor)\n",
    "    for n in range(N):\n",
    "        y[n * factor:(n + 1) * factor] = x[n]\n",
    "    return y\n",
    "\n",
    "# 定义上采样函数（线性插值法）\n",
    "def upsampling_linear_interpolation(x, factor):\n",
    "    N = len(x)\n",
    "    y = np.zeros(N * factor)\n",
    "    for n in range(N):\n",
    "        if n == 0:\n",
    "            y[0:factor] = x[0]\n",
    "        else:\n",
    "            for i in range(factor):\n",
    "                y[n * factor + i] = x[n - 1] + (i + 1) * (x[n] - x[n - 1]) / (factor + 1)\n",
    "    return y\n",
    "\n",
    "original_signal = np.zeros(10)\n",
    "original_signal[0] = 1.0\n",
    "for i in range(1, 10):\n",
    "    original_signal[i] = original_signal[i - 1] * 0.8\n",
    "\n",
    "# 使用零阶保持法以2为因子进行上采样\n",
    "upsampled_signal_zero_order = upsampling_zero_order_hold(original_signal, 2)\n",
    "\n",
    "# 使用线性插值法以4为因子进行上采样\n",
    "upsampled_signal_linear = upsampling_linear_interpolation(original_signal, 4)\n",
    "\n",
    "# 可视化原始信号和上采样后的信号\n",
    "plt.figure(figsize=(12, 8))\n",
    "plt.subplot(3, 1, 1)\n",
    "plt.stem(original_signal)\n",
    "plt.title('Original Impulse Response Signal')\n",
    "plt.ylabel('Amplitude')\n",
    "\n",
    "# 零阶保持法\n",
    "plt.subplot(3, 1, 2)\n",
    "plt.stem(upsampled_signal_zero_order)\n",
    "plt.title('Upsampled Signal (Zero-Order Hold, Factor = 2)')\n",
    "plt.xlabel('Sample Index')\n",
    "plt.ylabel('Amplitude')\n",
    "\n",
    "# 线性插值法\n",
    "plt.subplot(3, 1, 3)\n",
    "x_axis = np.arange(len(upsampled_signal_linear))\n",
    "interpolated_points = []\n",
    "for i in range(0, len(x_axis), 2):\n",
    "    interpolated_points.append(upsampled_signal_linear[i])\n",
    "plt.stem(x_axis[::2], interpolated_points)\n",
    "plt.title('Upsampled Signal (Linear Interpolation, Factor = 4)')\n",
    "plt.xlabel('Sample Index')\n",
    "plt.ylabel('Amplitude')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd1bf890",
   "metadata": {},
   "source": [
    "# 下采样"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d661baef",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 定义下采样函数\n",
    "def downsampling(x, factor):\n",
    "    N = len(x)\n",
    "    y = np.zeros(N // factor)\n",
    "    for n in range(N // factor):\n",
    "        y[n] = x[n * factor]\n",
    "    return y\n",
    "\n",
    "# 这里生成一个简单的先上升后下降的冲击序列作为示例\n",
    "original_signal = np.zeros(20)\n",
    "original_signal[0] = 0\n",
    "for i in range(1, 10):\n",
    "    original_signal[i] = i * 0.1\n",
    "for i in range(10, 20):\n",
    "    original_signal[i] = (20 - i) * 0.1\n",
    "\n",
    "# 进行下采样（以2为因子下采样）\n",
    "downsampled_signal = downsampling(original_signal, 2)\n",
    "\n",
    "# 原始信号\n",
    "plt.figure(figsize=(10, 6))\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.stem(original_signal)\n",
    "plt.title('Original Impulse Response Signal')\n",
    "plt.ylabel('Amplitude')\n",
    "\n",
    "#下采样后的信号\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.stem(downsampled_signal)\n",
    "plt.title('Downsampled Signal (Factor = 2)')\n",
    "plt.xlabel('Sample Index')\n",
    "plt.ylabel('Amplitude')\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
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